Not sure what you mean by "moving parts", but I don't think the 700 is any "simpler" than the M70. To accurize an action on the basic level, the action is squared up and trued to accept a trued barrel. The bolt lugs are also lapped for good and equal contact.
Beyond that, the raceway is sometimes modified. With the 700, many (including myself) replace the stock bolt with a one piece bolt (safety and function issue) and upgraded extractor (function issue). They also replace the recoil lug with a heavier duty tapered lug and have it pinned to the receiver which a basic function issue that will affect accuracy if the lug starts to deform under stress, which does sometimes happen, especially with more potent chamberings.
The M70 and Vanguard/Howa both have integrated recoils that are made as part of the receiver.
The Howa/Vanguard actions have one piece, ported bolts with M16 style extractors.
Another thing about the M70 and Howa is they have flat bottom reciever which many believe are a better design than round bottom receivers because they better resist the twisting action that occurs when a bullet is sent down a rifled barrel.
Triggers. I have worked on 700, M70 and Vanguard triggeres. The M70 being the simplest and easiest to tune followed by the Vanguard. The (old style) 700 triggers were a PITA to tune and also a PITA to remove and put back. The Vanguard is the easiest to remove and put back - one screw. I was able to tune both my Senderos to about 2 1/2 lbs, the M70 to 1 lb and the Vanguards to 1.5 lbs. The new Vanguard trigger is a better trigger overall, two stage with 3 position safety, easy to tune - 1 screw and very crisp. Unfortunately, the one I got will only tune down to about 3 lbs. I might clip out a coil in the spring to lighten it or replace it with a Timney but for now it works well enough.
I just recently picked up a new Vanguard (the one referred to above) in 223 and it's a great shooter. 1/2 MOA
IMO, actions are probably the component that least least affect the accuracy of a rifle with the barrel and stock being the most important components. The bedding of the action is of course very important.
I've said before that any action can be made to function well in an accurate rifle. It's just a matter of how much time and $$$ you have to put into it. In my experience the Vanguard action have cost much less and the only thing I have replaced is the trigger - not out of necessity (already tuned to a crisp 1.5 lbs), but out of preference for a 3 position trigger for a hunting rifle.
One of my early rifles was an M77 (Tang Safety) 7mm RM. It served me very well as a short to mid range hunting rifle. With handloads, I got about 3/4 MOA until I burned the barrel out. Now it just sits here retired. If i do get it rebarreled it will be because of sentimental value and not because I like the action. The angled front action screw is a problematic design and recoil lug, although integrated is smallish. The scope mount design is a good one but does not allow for a one peice base unless you had one custom made. Also very limited choice of rings due to it's proprietary design.
Hope that helps the OP. Sorry I could not comment on the Savage action.